6 papers
Relative entropy technique in terms of position and momentum and its application to Euler-Poisson system
Jan Giesselmann, Kiwoong Kwon, Min-Gi Lee
This paper presents a systematic study of the relative entropy technique for compressible motions of continuum bodies described as Hamiltonian flows. While the description for the…
Solutions of Schrödinger equations with symmetry in orientation preserving tetrahedral group
Ohsang Kwon, Min-Gi Lee
We consider the nonlinear Schrödinger equation \begin{equation*} Δu = \big( 1 +\varepsilon V_1(|y|)\big)u - |u|^{p-1}u \quad \text{in} \quad \mathbb{R}^N, \quad N\ge 3, \quad p \in…
Infinitely many segregated vector solutions of Schrodinger system
Ohsang Kwon, Min-Gi Lee, Youngae Lee
We consider the following system of Schrödinger equations \begin{equation*}\left.\begin{cases} -ΔU + λU = α_0 U^3+ βUV^2 -ΔV + μ(y) V = α_1 V^3+βU^2V \end{cases}\right. \text{in} \…
Localization in adiabatic shear flow via geometric theory of singular perturbations
Min-Gi Lee, Theodoros Katsaounis, Athanasios Tzavaras
We study localization occurring during high speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition am…
Existence of localizing solutions in plasticity via geometric singular perturbation theory
Min-Gi Lee, Athanasios Tzavaras
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attenti…
Localization in inelastic rate dependent shearing deformations
Theodoros Katsaounis, Min-Gi Lee, Athanasios Tzavaras
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into…